Rare Disasters, Credit and Option Market Puzzles

Abstract

We embed systematic default, pro-cyclical recovery rates and habit persistence into a model with a slight possibility of a macroeconomic disaster of reasonable magnitude. We derive analytical solutions for defaultable bond prices and show that a single set of structural parameters calibrated to the real economy can simultaneously explain several key empirical regularities in equity, credit, and options markets. Our model captures the empirical level and volatility of credit spreads, generates a fl‡exible credit risk term structure, and provides a good fi…t to a century of observed spreads. The model also matches high-yield and CDO tranche spreads, equity market moments, and index option skewness. Finally, our model implies a time-varying relationship between bond and option prices that depends on the state of the economy and that explains the con‡flicting empirical evidence found in the literature.

Keywords: Credit spreads, volatility, term structure, option skewness, stochastic recovery, consumption risk

JEL Classification: C60, G12, G13